Suppsedly to eventually offer more advanced file sharing capabilities (edit history, etc.)
On the server side, many web servers have plugins to support it.
On the client side, Win2 K does a very nice job at the OS level. In many other platforms, a specific client app is needed. (In MsWindows pre-2K, there's a version of MsIE that has some WebDAV support, but it's much uglier.)